Percentage Increase Calculator

What this calculator does

Here you start with one number and a rate, not two numbers to compare. A price before 15% tax goes on, a salary before a 5% raise, a figure you need to grow by a set percent. What does it become once the percentage is added?

Type the original value and the percent to add, and the tool gives you the new, larger amount, along with how much got added on.

Using the calculator

1. Type the original value.
2. Type the percentage to increase by.
3. Press Calculate.

The percentage must be above zero. You get two numbers back: the increased value, and the absolute difference, which is simply the amount that was added on.

The formula | original + (original × percent) ÷ 100

The increased value is:

original + (original × percent) ÷ 100

Work out the percentage of the original value, then add it back on. The first part, (original × percent) ÷ 100, is the amount added, which the tool also reports. The same calculation can be written as original × (1 + percent ÷ 100), multiplying the original by a single factor.

A worked example | 40 increased by 20%

Say you start with 40 and increase it by 20%.

1. The amount to add: (40 × 20) ÷ 100 = 8.
2. Add it on: 40 + 8 = 48.

So 40 increased by 20% is 48, with an added amount of 8. If that 20% were a sales tax, 48 would be the price including tax.

Applying a percent, or finding one

There are two opposite percentage questions, and it is worth being clear which one you have. This tool applies a percentage you already know: "what is 40 increased by 20%?" gives 48. The other direction finds the percentage from two values you already have: "something grew from 70 to 120, what percent increase is that?" For that, use the percent increase calculator. One starts with a percent and produces a new value; the other starts with two values and produces a percent.

Applying two increases in a row

If you increase a value and then increase the result again, the second increase works on the already-larger amount, not the original. So the two do not simply add together. A 10% rise followed by another 10% rise on 100 gives 110, then 121, an 11 rise the second time, not 10. Successive increases build on each other.

Questions people ask

What is 40 increased by 20%?

48. Add 20% of 40, which is 8, onto the 40.

What is the formula?

original + (original × percent) ÷ 100, which is the same as original × (1 + percent ÷ 100).

How is this different from the percent increase calculator?

This one applies a percent you give to a value. The percent increase calculator works the other way, finding the percent between two values you already have.

What is the absolute difference it shows?

The amount added, (original × percent) ÷ 100. For 40 increased by 20%, it is 8.

If I apply 10% twice, is that 20%?

No. The second 10% is taken on the already-increased value, so 100 becomes 110 and then 121, a 21% increase overall.

References

A note on the idea behind it. Increasing a value by a percentage adds that percentage of the value back on, equivalent to multiplying by the factor 1 + percent ÷ 100. This is distinct from finding the percentage increase between two known values. For further reading, see Relative change and difference.

1. Applying a percentage increase, original × (1 + percent ÷ 100), to raise a value by a known rate.